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Rollout statistics

Posted By: Timothy Chow
Date: Sunday, 19 November 2023, at 11:53 p.m.

In Response To: pay now? How come? (Sam Pottle)


This is the sort of question that Rollout Statistics are designed to address. I did a 10000-game rollout of 8/7 8/2 and 11/4. The move 11/4 effectively creates a "last-roll position": if White hits, then she doubles Blue out, and if White misses, then Blue doubles White out. Since White is a favorite to miss, Blue is an equity favorite, and we can calculate his equity exactly; it's 1/9.

After 8/7 8/2, the situation is more complicated. White still doubles Blue out when she hits, but if she misses then it's D/T and Blue gets some value out of the cube. You can see this below in the Rollout Statistics. White doubled Blue out immediately in 3057 of the 10000 trials. Of the remaining trials, Blue won a single 4373 times with the cube on 2; when things went poorly for Blue, he usually (1993 times) just passed White's redouble to 4. 

 

Cube	Win BG	Win G	Win S	Cash	Pass	Lose S	Lose G	Lose BG 

1					3057				 

2	3	183	4373		1993	7	92	6	 

4		9	2	58		185	16	 

8			11		2	1	 

16						2

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